Having Fun

have the time of one's life
めちゃめちゃ楽しく過ごす

Example:
Yesterday on the mountain slope, I had the time of my life.
昨日の山はすごく楽しかった。

Comment:
An extremely high level fun. Probably most often used for a first-time activity that someone has never experienced before.

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have a blast
すごく楽しく過ごす

Example:
I had a blast at the concert last night.
昨日のコンサートは凄く楽しかったよ。

Comment:
A very high level fun. Probably most often used for an energetic activity.

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have a swell time
けっこう楽しく過ごす

Example:
I had a swell time at your uncle's.
君のおじさんの所に結構楽しかった。

Comment:
A medium fun. Probably most often used when you expect not to have fun, but the activity turns out to be fun.

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have a good time
楽しく過ごす

Example:
I had a good time; let's do this again sometime.
楽しかったわ。またいつかやろう。

Comment:
A low fun. Probably most often used for a relaxing activity.

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enjoy
楽しく過ごす

Example:
I enjoyed the movie tonight.
あの映画が楽しかった。

Comment:
A normal fun. But you probably knew that already.